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Task-oriented dialogue-based spatial reasoning systems need to maintain history of the world/discourse states in order to convey that the dialogue agent is mentally present and engaged with the task, as well as to be able to refer to earlier states, which may be crucial in collaborative planning (e.g., for diagnosing a past misstep). We approach the problem of spatial memory in a multi-modal spoken dialogue system capable of answering questions about interaction history in a physical blocks world setting. We employ a pipeline consisting of a vision system, speech I/O mediated by an animated avatar, a dialogue system that robustly interprets queries, and a constraint solver that derives answers based on 3D spatial modelling. The contributions of this work include a semantic parser competent in this domain and a symbolic dialogue con- text allowing for interpreting and answering free-form historical questions using world and discourse history.